Method and apparatus for measuring color

ABSTRACT

The invention relates to apparatus for measuring color, the apparatus comprising: an acquisition system including a video camera and processing means organized to respond to the signals delivered by the camera to determine the tristimulus values of the color of the object in a reference calorimetric system by using a transfer matrix to transform the calorimetric system associated with said acquisition system into the reference calorimetric system, and to determine a correction function Γ to correct the non-linearities of said acquisition system.

BACKGROUND OF THE INVENTION

[0001] To measure the color of an opaque object, it is known to use acalorimeter comprising a light source for illuminating the object,optical analyzer apparatus for analyzing the light reflected by theobject, and calculation means responsive to the signals delivered by theoptical analyzer apparatus to determine the tristimulus values X, Y, andZ of the color of the object in a reference colorimetry system, forexample the system adopted in 1931 by the International Commission onIllumination (CIE).

[0002] The optical analyzer apparatus includes means for splitting thelight reflected by the object into three beams, each of which passesthrough a filter system and terminates on an associated photoelectriccell.

[0003] That type of known calorimeter suffers from the drawback ofrequiring direct contact between the optical analyzer apparatus and theobject whose color is to be measured, and of being unsuited to measuringthe color of an object remotely or to measuring the color of an objectthat is not opaque, that diffuses or absorbs light while also passing aportion thereof, such as the skin or certain plastics or kinds ofmakeup.

[0004] To mitigate those drawbacks, attempts have been made to measurecolor by means of a video camera.

[0005] Nevertheless, so far as the Applicant company is aware, therestill does not exist any apparatus which is suitable for remotelymeasuring the color of an object, in particular an object that is notopaque, and which is capable of measuring color accurately, reliably,and quickly while nevertheless being of relatively low price.

OBJECTS AND SUMMARY OF THE INVENTION

[0006] A particular object of the present invention is to provide novelapparatus for measuring the color of any type of object, using a videocamera, and making it possible to measure color accurately, reliably,and quickly while being of relatively low cost and easy to use.

[0007] The invention achieves this by means of an apparatus formeasuring color, comprising:

[0008] an acquisition system including a video camera, said acquisitionsystem being suitable for delivering signals representative of thetristimulus values in a calorimetric system associated with saidacquisition system for the color of an object placed in the observationfield of the camera; and

[0009] processor means organized to respond to said signals to determinethe tristimulus values of the color of the object in a referencecolorimetric system using a transfer matrix to transform from thecalorimetric system associated with said acquisition system into thereference calorimetric system, and a correction function for correctingthe non-linearities of said acquisition system, said transfer matrix andsaid correction function being calculated using an iterative processbased on the known tristimulus values in the reference calorimetricsystem of three primary colors and of at least two gray levels and fromtheir tristimulus values in the colorimetric system associated with saidacquisition system, as obtained by using said video camera to observesaid primary colors and said gray levels.

[0010] In a preferred embodiment of the invention, the apparatus furtherincludes a display system for reproducing all or a portion of the imageobserved by said video camera after said signals delivered by theacquisition system have been processed by said correction function.

[0011] Preferably, said display system includes a cathode ray tube (CRT)display device.

[0012] Advantageously, the apparatus further comprises a light sourcefor illuminating the object placed in the field of observation of thecamera, said source having a continuous emission spectrum I(λ) selectedso as to be close to a reference illuminant of spectrum D(λ).

[0013] The camera includes a set of optical filters of spectra FR(λ),FG(λ), and FB(λ) to resolve the image observed by the camera intoprimary color images on the sensors of said camera, advantageously thesource is filtered by one or more filters for which the resultant filterfunction F(λ) is selected so as to minimize the error of differencesbetween the products D(λ).x(λ), D(λ).y(λ), and D(λ).z(λ), and a linearcombination of the products:

[0014] F(λ).I(λ).FR(λ), F(λ)I(λ).FG(λ), and F(λ).I(λ).FB(λ) where x(λ),y(λ), and z(λ) are the spectral tristimulus values in the referencecalorimetric system.

[0015] Preferably, said reference illuminant is the CIE illuminant ofspectral D₆₅(λ).

[0016] The invention also provides a method of measuring the color of anobject from an acquisition system including a video camera suitable fordelivering signals representative of the tristimulus values, in acolorimetric system associated with the said acquisition system, of thecolor of an object placed in the field of observation of the camera, themethod comprising the steps consisting in:

[0017] successively or simultaneously placing in the field ofobservation of the camera three primary colors and at least two graylevels, the tristimulus values of said primary colors and of said graylevels being known in a reference calorimetric system;

[0018] using an iterative process based on said tristimulus values insaid reference colorimetric system and the corresponding tristimulusvalues in the calorimetric system associated with said acquisitionsystem as obtained by observing said primary colors and said gray levelsusing said camera to calculate a transfer matrix for transforming fromthe calorimetric system associated with said acquisition system into thereference calorimetric system, and also a correction function forcorrecting the non-linearities of said acquisition system; and

[0019] determining the tristimulus values in the reference calorimetricsystem of the color of an object placed in the field of observation ofthe camera by using said transfer matrix and said correction function ascalculated.

[0020] Advantageously, in the method, the color of the object is alsoviewed by means of a display system after the non-linearities of theacquisition system have been corrected.

[0021] Advantageously, in this method, the non-linearities of thedisplay system are also corrected.

[0022] In a particular implementation of the method of the invention,the display system includes a CRT display device.

[0023] In a particular implementation of the method of the invention, afunction for correcting the non-linearities of the display system isdetermined by:

[0024] displaying two zones having the same color but with luminancesthat may be different, the color of one of the zones being obtained byjuxtaposing pixels having distinct control levels and the color of theother zone being obtained by a set of pixels all having the same controllevel corresponding to the mean of the control levels of the pixels ofthe other zone; and

[0025] making the luminances of the two zones equal for an observer byacting on pixel control level in one of the zones.

[0026] From the values of the pixel control levels in each of said zonesbefore and after luminance equalization, information is deduced forcalculating said correction function for correcting the non-linearitiesof the display system.

[0027] Preferably, one of the zones is rasterized.

[0028] Advantageously, said rasterized zone has every other raster lineblack.

[0029] When the display system includes a CRT display device and at acontrol level transition for pixels in the same raster line giving riseto a change in luminance between at least one pixel in said raster lineand the pixel immediately following it, in the raster scanningdirection, the control level for said immediately following pixel isadvantageously selected as a function of the rate at which the controlsignal for the electron beam reaching pixels situated on the same rasterline varies when the pixel control level varies.

[0030] To determine the correction to be made to take account of therate at which the signal controlling the electron beam reaching pixelssituated on the same raster line varies, it is advantageous to proceedas follows.

[0031] Two zones of the same color but of luminances that may bedifferent are displayed, the color of one of the zones being obtained byjuxtaposing on the same-raster line pixels of different control levels,and the color of the other zone being obtained by a set of pixels allhaving the same control level, then the luminances of the two zones aremade equal for an observer by acting on pixel luminance control level inone of the zones.

[0032] From the values of the pixel luminance control levels in each ofsaid zones before and after equalization, information is deduced forcalculating the correction to be provided in order to take into accountthe rate at which the control signal for the electron beam reaching thepixels situated in the same raster line varies when the pixel controllevel varies.

[0033] Preferably, the zone formed by juxtaposing pixels of differentluminances comprises, in the scan direction, alternating pixels each ofluminance set to a level different from that of the preceding pixel.

[0034] The invention also provides a method of correcting the responseof a display device having raster lines of pixels, in which, at atransition in the control level for pixels in the same raster line thatgives rise to a variation of luminance at least between a pixel of saidraster line and the pixel immediately following it in the rasterscanning direction, the control level of said immediately followingpixel is selected as a function of the rate at which the luminance ofpixels situated on the same raster line varies when the control level ofsaid pixels varies.

[0035] Advantageously, a correction function is determined forcorrecting the non-linearities of said display device by:

[0036] displaying two zones having the same color but luminances thatmay be different, the color of one of said zones being obtained byjuxtaposing pixels having different control levels, while the color ofthe other zone is obtained by a set of pixels all having the samecontrol level;

[0037] making the luminances of the two zones equal for an observer byacting on the pixel control levels of one of the zones; and

[0038] from the values of the pixel control levels of each of saidzones, deducing information for calculating said correction function forcorrecting the non-linearities of the display device.

[0039] In a particular implementation of this method, said zone made upof pixels having different control levels is rasterized.

[0040] Advantageously, said rasterized zone includes raster lines inwhich every other raster line is black.

[0041] In another particular implementation of the method, said zonemade up of pixels having different control levels includes alternatingpixels in each raster line having a control level that is different fromthe control level of the preceding pixel in said raster line.

[0042] Also, in a particular implementation of the method of theinvention, the above-mentioned iterative process comprises the stepsconsisting in:

[0043] calculating an approximate transfer matrix on the basis of theknown tristimulus values of said primary colors and of said gray levels,and on the basis of an approximate correction function;

[0044] calculating a new approximate correction function using theapproximate transfer matrix calculated in this way and the knowntristimulus values of said gray levels, and by interpolating the missingvalues; and

[0045] recalculating the approximate transfer matrix and the approximatecorrection function until a fixed convergence threshold is reached.

[0046] In a variant, the iterative process comprises the stepsconsisting in:

[0047] calculating an approximate correction function on the basis ofthe known tristimulus values of said primary colors and of said graylevels, and on the basis of an approximate transfer matrix;

[0048] calculating a new approximate transfer matrix using the knowntristimulus values of said grays and interpolating the missing values;and

[0049] recalculating the approximate correction function and theapproximate transfer matrix until a fixed convergence threshold isreached.

[0050] Advantageously, non-uniformities in the illumination of theobject by the source are also corrected, as are optical aberrations ofthe camera, by measuring the luminance of the screen at various pointsand by comparing it with the luminance at a reference point, e.g. thecenter of the image.

BRIEF DESCRIPTION OF THE DRAWINGS

[0051] The invention will be better understood on reading the followingdetailed description of a non-limiting embodiment of the invention, andon examining the accompanying drawings, in which:

[0052]FIG. 1 is a diagrammatic view of color measuring apparatusconstituting an embodiment of the invention;

[0053]FIG. 2 is a model of the acquisition system;

[0054]FIG. 3 is a model of the processing that enables the tristimulusvalues in the reference colorimetry system to be determined;

[0055]FIG. 4 is a flow chart showing the iterative process forcalculating the transfer matrix and a correction function for correctingthe non-linearities of the acquisition system;

[0056]FIG. 5 is a model of the processing enabling corrected tristimulusvalues to be determined in the colorimetry system associated with thedisplay system;

[0057]FIG. 6 is a model of the processing applied to the input signalsin a CRT display device;

[0058]FIGS. 7 and 8 show two test patterns for calibrating the-displaysystem; and

[0059]FIGS. 9 and 10 are diagrams showing how luminance variation inpixels on the same raster line varies as a function of variation in thecontrol level applied to the pixels, respectively with and withoutanticipated correction for taking into account the rate at which thesignal controlling the electron beam reaching the pixels varies when thecontrol level varies.

MORE DETAILED DESCRIPTION

[0060]FIG. 1 shows apparatus constituting a non-limiting embodiment ofthe invention and enabling the color of an object 0 to be measuredremotely.

[0061] The apparatus 1 comprises a video camera 2, a microcomputer 3,and a cathode ray tube (CRT) display device 4.

[0062] The camera 2 has three CCD type sensors 8, 9, and 10 suitable fordelivering respective analog electric signals V_(R), V_(G), and V_(B),representative of red, green, and blue levels at each point of the imageobserved and scanned by the camera 2, in conventional manner.

[0063] A light source 7 serves to illuminate the object 0 placed in thefield of the camera 2. Advantageously, a xenon light source is usedwhich comes close to the D₆₅(λ) spectrum as defined by the CIE.

[0064] The microprocessor 3 includes a central processor unit 5 and athree-channel analog-to-digital converter 6 connected to the centralunit 5 and enabling the analog signals V_(R), V_(G), and V_(B) deliveredby the camera 2 to be converted into digital form.

[0065] The signals converted into digital form and respectivelyreferenced R, G, and B are then applied to the central unit 5.

[0066] In the particular example described, each of the signals R, G,and B is encoded on 8 bits, and the data acquired by the camera at eachimage point is constituted by a triplet (R, G, B) of three integers eachlying in the range 0 to 255.

[0067] Naturally, it would not go beyond the ambit of the invention toencode the signals on some other number of bits.

[0068] The camera 1 and the converter 6 constitute an acquisition systemwhich is modelled in FIG. 2.

[0069] The light spectrum reflected from each point of the object 0 andobserved by the camera is the product of the spectrum of the lightsource I(λ) multiplied by the reflectance spectrum Re(λ) at said point.

[0070] The optical system of the camera 2 has three optical filters ofrespective spectra FR(λ), FG(λ), and FB(λ) to resolve the image observedby the camera onto the CCD sensors 8, 9, and 10 in the form of images inthe primary colors red, green, and blue.

[0071] The electronic components of the acquisition system contributenoise that can be resolved into an AC component and a DC component, withthe noise in each of the channels being written NR, NG, and NB.

[0072] The high and low digitizing levels for each of the channels 11,12, and 13 in the converter 6 are adjustable.

[0073] The low digitizing level in each channel is adjusted so as toeliminate the DC component of the noise, and the procedure is to ensurethe lens cap is in place on the camera and then increase progressivelythe low digitizing level until the darkest zone of the image correspondsto the converter outputting a digital signal equal to unity on eachchannel.

[0074] The high digitizing level is adjusted by placing the brightestobject liable to be observed in the field of observation of the camera.

[0075] It is advantageous to use a white surface.

[0076] The high digitizing level is adjusted until the brightestobserved zone on the image corresponds to each channel of the exampledescribed outputting the maximum value of its digital signal minusunity, i.e. outputting the value 254.

[0077] If necessary, the brightness of the source 7 is reduced if thehigh level cannot be adjusted in the above manner.

[0078] AC noise can be attenuated by averaging a plurality of successiveacquisitions of the same image.

[0079] The digital signals (R, G, B) delivered by the converter 6 areprocessed in the central unit 5 to determine, at each point of the imageobserved by the camera 2, the tristimulus values in a referencecolorimetry system, such as the XYZ colorimetry system of the CIE. Thisprocessing corrects the non-linearities in the acquisition system, i.e.essentially the non-linearities of the CCD sensors 8, 9, and 10, andalso the non-linearities of the converter 6. This processing alsoadvantageously corrects non-uniformity of illumination of the object 0by the source 7, and optical aberrations of the camera 2.

[0080] Naturally, it would not go beyond the ambit of the invention toselect a reference colorimetry system other than the XYZ colorimetrysystem of the CIE.

[0081]FIG. 3 models the processing performed by the central unit 5.

[0082] Υ_(R), Υ_(G), and Υ_(B) designate the components of the functionΥ for correcting the non-linearities of the CCD sensors 8, 9, and 10 andof the converter 6 in each of the red, green, and blue channels.

[0083] The transfer function for transforming the calorimetric systemassociated with the acquisition system into the reference colorimetricsystem can be written in the form of a matrix M.

[0084] X, Y, and Z represent the tristimulus values in the referencecolorimetric system.

[0085] FX(i, j), FY(i, j), and FZ(i, j) designate the functions forcorrecting non-uniformity in the illumination of the object by thesource 7, and for correcting optical aberrations of the camera 2, as afunction of the coordinates (i, j) of each point under consideration inthe image.

[0086] The coefficients of the matrix M and the components Υ_(R), Υ_(G),and Υ_(R) are calculated in the manner described below with reference tothe algorithm shown in FIG. 4.

[0087] Initially, in step 14, a first data set is acquired for use inthe subsequent processing, by placing successively or simultaneously inthe field of observation of the camera n calorimetric samplescorresponding to different gray levels with known tristimulus values (X,Y, Z) in the reference calorimetric system XYZ.

[0088] Then, in the next step 15, three calorimetric samplescorresponding to three primary colors with known tristimulus values inthe reference calorimetric system are placed successively orsimultaneously in the field of view to acquire a second data set forsubsequent use in the processing. The tristimulus values in thereference colorimetry system can be measured using a spectrophotometer.

[0089] By way of example, the primary colors can be red, green, andblue, or magenta, cyan, and yellow. In general, they can be any colorsproviding they form a base in the reference calorimetric system.

[0090] The primary colors are preferably selected in such a manner thatthe triangle they form in the plane of the chromatic diagram for thereference colorimetric system encompasses all of the colors that are tobe measured.

[0091] The calorimetric samples used are preferably opaque and ofuniform color, and therefore measurable using a conventional colorimeteror spectrophotometer.

[0092] The various grays and primary colors are preferably measured inthe center of the observation field of the camera 2 over an area that issufficiently small, preferably constituting only about 10% of the totalarea covered by the field of observation of the camera, and which can beconsidered as being illuminated in uniform manner by the source 7.

[0093] Preferably, in order to acquire the various grays and primarycolors, the positions of the source 7 and of the camera 2 relative tothe samples, and also the type of lighting used, are as close aspossible to the measurement configuration used by the calorimeter orspectrophotometer for determining the tristimulus values of the colorsof the calorimetric samples used in the reference calorimetric system.

[0094] In step 14, the acquisition system delivers signalsrepresentative of the tristimulus values of n gray levels in the form oftriplets of values which are written, in simplified manner: RE₁, RE₂, .. . , RE_(n), and the corresponding triplets in the referencecalorimetric system are respectively written, likewise in simplifiedmanner, as: XE₁, XE₂, . . . , XE_(n).

[0095] The notation RE_(i) designates a triplet of values (R, G, B) andthe notation XE_(i) designates the corresponding triplet of values (X,Y, Z).

[0096] In step 15, the acquisition system delivers triplets oftristimulus values RC₁, RC₂, and RC₃, which triplets correspond in thereference calorimetric system to XC₁, XC₂, and XC₃, respectively, usingthe same type of notation as above.

[0097] In step 16, an iteration parameter k is initialized to the value0, and in step 17, an approximate correction function Υ^(k) isinitialized with components Υ_(R) ^(k), Υ_(G) ^(k), and Υ_(B) ^(k),which function may vary on each iteration.

[0098] At iteration k=0, Υ_(R) ⁰, Υ_(G) ⁰, and Υ_(B) ⁰ are selected tobe equal to the identity function.

[0099] In step 18, for each iteration k, an approximate matrix P^(k) iscalculated for converting from the reference colometric system XYZ intothe colorimetric system associated with the acquisition system by theformula:

P^(k)(Υ^(k))([RC₁RC₂RC₃])[XC₁XC₂XC₃]⁻¹

[0100] In step 19, the n values of the approximate correction functionΥ^(k) are calculated using the formula:

(Υ^(k)(RE_(i))=P^(k)XE_(i) for i going from 1 to n.

[0101] In step 20, the values missing from the correction function Υ^(k)at iteration k are interpolated as follows.

[0102] For example, for the component Υ_(R) ^(k):

[0103] if Υ_(R) ^(k)(ω₀) is known and if Υ_(R) ^(k)(ω₁) is known,

[0104] then for ω₀<ω<ω₁,

[0105] Υ_(R) ^(k)(ω) is determined by the following formula:

log(Υ_(R) ^(k)(ω)/255)=((ω−ω₁)/(ω₀−ω₁)·log(Υ_(R)^(k)(ω₀)/255)+((ω−ω₀)/(ω₀−ω₁))·log(Υ_(R) ^(k)(ω₁)/255)

[0106] The same is applied to Υ_(G) ^(k) and Υ_(B) ^(k).

[0107] In step 21, the correction functions Υ_(R) ^(k), Υ_(G) ^(k), andΥ_(B) ^(k) are normalized:

255.Υ_(R) ^(k)(ω)/Υ_(R) ^(k)(255)→Υ_(R) ^(k)(ω)

255.Υ_(G) ^(k)(ω)/Υ_(G) ^(k)(255)→Υ_(G) ^(k)(ω)

255.Υ_(B) ^(k)(ω)/Υ_(B) ^(k)(255)→Υ_(B) ^(k)(ω)

[0108] for ω going from 1 to n.

[0109] In step 22, the error e^(k) is calculated using the formula:

e^(k)(Σ((M^(k)Υ^(k)(RC_(i))−XC_(i))²)^(1/2)

[0110] for i going from 1 to n, with M^(k)=(P^(k))⁻¹.

[0111] In step 23, the iteration parameter k is incremented.

[0112] In step 24, a test is made to see whether the error e^(k) hasconverged.

[0113] If it has converged, the iterative process is stepped in step 25,otherwise the process returns to step 18 to calculate a new approximatetransfer matrix P^(k) and a new approximate function Υ^(k) forcorrecting non-linearities.

[0114] In step 25, the final transfer matrix M is calculated fortransforming the colorimetric system associated with the acquisitionsystem into the reference colorimetric system using the formula:

M=M^(k)=Υ^(k)([XC₁XC₂XC₃])[RC₁RC₂RC₃]⁻¹

[0115] The transfer matrix M and the function Υ for correctingnon-linearities are thus calculated using an iterative method in whicheach iteration calculates an approximate transfer matrix and anapproximate function for correction non-linearities.

[0116] Once the components Υ_(R), Υ_(G), and Υ_(B) of the function Υ forcalculating the transfer matrix M has been calculated, functions aredetermined for correcting non-uniformity in the illumination of theobject 0 by the source 7, and for correcting the optical aberrations ofthe camera, i.e. the above-mentioned function FX(i, j), FY(i, j), andFZ(i, j) are calculated.

[0117] The functions FX(i, j), FY(i, j), and FZ(i, j) are calculated byacquiring the image of an object of uniform color that occupies theentire field of observation of the camera, and by determining thecorrection to be provided in such a manner that all of the image pointshave the same tristimulus values as the center of the image.

[0118] More precisely, in the example described, the tristimulus valuesfor all of the points belonging to a measurement window are averaged,with said set of points being centered on a point having coordinates (i,j).

[0119] Mean values IMX(i, j), IMY(i, j), and IMZ(i, j) are thus obtainedand the functions FX(i, j), FY(i, j), and FZ(i, j) are obtained byapplying the following formulae:

FX(i, j)=IMX(i_(center), j_(center))/IMX(i, j)

FY(i, j)=IMY(i_(center), j_(center))/IMY(i, j)

FZ(i, j)=IMZ(i_(center), j_(center))/IMZ(i, j)

[0120] where (i_(center), i_(center)) are the coordinates of the centerof the image.

[0121] Transforming from (R, G, B) coordinates to (X, Y, Z) coordinatesas described above can impart a bias when the products D₆₅(λ).x(λ),D₆₅(λ).y(λ) and D₆₅(λ).z(λ) are not linear combinations of the productsI(λ).FR(λ), I(λ).FG(λ), and I(λ).FB(λ), as is usually the case.

[0122] In order to reduce this bias, the source can advantageously befiltered with an optical filter F defined in such a manner as tominimize the error of differences between the products D₆₅(λ).x(λ),D₆₅(λ).y(λ), and D₆₅(λ).z(λ) and a linear combination of the productsF(λ).I(λ).FR(λ), F(λ)I(λ).FG(λ), and F(λ).I(λ).FB(λ)

[0123] Such a filter serves to optimize color measurement and is matchedto the acquisition system.

[0124] It will be understood that the particular embodiment of theinvention described above makes it possible to discover accurately thecomponents (X, Y, Z) in the reference colorimetric system of an objectthat is placed in the field of observation of a video camera.

[0125] Thus, for example, it is possible to inspect, without makingphysical contact, articles such as receptacles or labels travelling athigh speed on a manufacturing line, with inspection serving to detectany change in the color of said objects or any surface defects.

[0126] It can also be advantageous to use a display system to reproduceaccurately the color of an object observed by the camera.

[0127] Advantageously, a color is simultaneously measured and accuratelyreproduced by the display system. Nevertheless, without going beyond theambit of the invention, it is possible to perform one or the other.

[0128] When all that is required is to reproduce the color of an objectaccurately by means of the display system, there is no need to displayto the user the tristimulus values of the color of the object in thereference calorimetric system as calculated by the central unit 5 in themanner described above.

[0129] Applying the output signals (R, G, B) from the converter 6directly to the input of the display system would lead to unsatisfactoryreproduction of the color of the object on the screen of the displaydevice 4, in particular because of the non-linearities in theacquisition system and because of the non-linearities in the displaysystem, and because of the differences between the calorimetric systemsassociated respectively with the acquisition system and with the displaysystem.

[0130] A first improvement is provided by correcting the non-linearitiesof the acquisition system, as described above.

[0131] Nevertheless, the quality with which the color of the object isreproduced can be further improved when the non-linearities of thedisplay system are also corrected.

[0132] This correction is performed in the central unit 5.

[0133]FIG. 5 shows a model of the processing for transformingtristimulus values (X, Y, Z) in the reference calorimetric system XYZinto tristimulus values (R′, G′, B′) at the input to the display system.

[0134] The process begins by transforming the previously determinedtristimulus values (X, Y, Z) into tristimulus values in the calorimetricsystem associated with the display system by means of a transfer matrixM′, and then each of the values obtained in this way has a correctionfunction Υ′ applied thereto which is not related to position on thescreen, which function has components Υ_(R)′, Υ_(G)′, and Υ_(B)′, andthen a function is applied for correcting non-uniformity of screenillumination FR(i, j), FG(i, j), and FB(i, j) which is associated withposition on the screen.

[0135]FIG. 6 shows a model of the processing applied to the digitalsignals (R′, G′, B′) received by the display system which leads to animage being obtained on the screen of the display device.

[0136] The tristimulus values (R′, G′, B′) for each image point aretransformed into analog signals by means of a three-channeldigital-to-analog converter 26, 27, and 28. The analog signals outputfrom the converter are processed in conventional manner at 29 so thateach of them controls a cathode beam for illuminating phosphorescentregions of the screen that respond to the incident electron flux byemitting light of a determined color. Summing the spectra R(λ), G(λ),and B(λ) emitted by the phosphorescent regions, respectively producingthe colors red, green, and blue, gives rise to a resultant spectrum E(λ)for each image point.

[0137] This transfer matrix M′ is calculated by knowing the tristimulusvalues (X_(R′), G_(R′), Z_(R′)), (X_(G′), Y_(G′), Z_(G′)) and (X_(B′),Y_(B′), Z_(B′)) in the reference colorimetric system XYZ of input colorscorresponding respectively to the following triplets (255, 0, 0), (0,255, 0), and (0, 0, 255) for each image point.

[0138] The transfer matrix M′ has column vectors comprising thecoordinates in the reference colorimetirc system for the three primarycolors under consideration. $M^{\prime} = \begin{matrix}{X_{R^{\prime}},} & {X_{G^{\prime}},} & X_{B^{\prime}} \\{Y_{R^{\prime}},} & {Y_{G^{\prime}},} & Y_{B^{\prime}} \\{Z_{R^{\prime}},} & {Z_{G^{\prime}},} & Z_{B^{\prime}}\end{matrix}$

[0139] To calculate the components Υ′_(R), Υ′_(G), and Υ′_(B) of thecorrection function Υ′, and knowing the matrix M′, it is possible to usea screen calorimeter to measure the light emitted at the center of theimage as a function of successive and different input triplet values(R′, G′, B′).

[0140] It is also possible to determine the components Υ′_(R), Υ′_(G),and Υ′_(B) without screen color measurement, as follows.

[0141] Account is taken of the fact that the luminance W from eachscreen point is associated with the voltage V controlling the electronbeam reaching it by the following approximate formula:

log(W/W _(max))=k ₁ +k ₂ log(V/V _(max))+k ₃(log(V/V _(max))² +k₄(log(V/V _(max)))³

[0142] Two ranges of input values R′, G′, or B′ are then distinguished:[0, 64] and [64, 255].

[0143] In each range, the parameters k₁, k₂, k₃, and k₄ are determinedby the luminance value when the input digital signal has the followingvalues in succession: 0, 32, 64, 128 in the first range, and 32, 64,128, 255 in the second.

[0144] By way of example, it is assumed that the procedure begins byseeking to determine the component Υ′_(R).

[0145] A test pattern of the kind shown in FIG. 7 is displayed on thescreen which pattern comprises a central rectangle of red colorcorresponding to an input selection (128, 0, 0). The central rectangleis included in a rasterized rectangle where every other line is of a redcolor corresponding to an input of (255, 0, 0) and where every otherline is of a black color corresponding to input values of (0, 0, 0).

[0146] Thereafter, and where appropriate, the input digital signal (R′,0, 0) controlling the luminance of the central rectangle is controlleduntil the luminance thereof appears to be equal to the luminance of therasterized rectangle.

[0147] Thereafter, the correction is deduced that ought to have beenapplied to the input signal in order to obtain such equalization in thevalue of the function Υ′_(R)(128).

[0148] The procedure is then repeated by displaying a central rectangleof color (64, 0, 0) surrounded by a rasterized rectangle where everyother line is of a red color corresponding to (Υ′_(R)(128), 0, 0) andthe intermediate lines being black in color, thereby making it possibleto calculate Υ′_(R)(64), etc . . . .

[0149] Thereafter, the values of the parameters k₁, k₂, k₃, and k₄ aredetermined and the missing values of Υ′_(R) are calculated from thepreceding formula.

[0150] The same procedure is applied for calculating Υ′_(G) and Υ′_(B).

[0151] Non-uniformity in screen illumination is due mainly to thedispersion of the electron beam that strikes the screen.

[0152] In order to correct this non-uniformity, the luminance andvarious points of the screen is measured for each of the three channels:red, green, and blue.

[0153] For each of the red, green, or blue channels, correction factorsare calculated to be applied to each point on the screen.

[0154] The correction factors for each of the red, green, and bluechannels are written FR(i, j), FG(i, j), and FB(i, j) respectively.

[0155] It is assumed that the screen is calibrated in the center, sothat it suffices to know the correction factors to be applied to eachpoint of coordinates (i, j) on the surface of the screen away from thecenter in order to obtain a screen that is calibrated in full.

[0156] The illumination of the screen as a function of the coordinates(i, J) of a point away from the center and of the coordinatesi_(center), j_(center) at the center of the screen varies approximatelywith the following function C(i, j):

C(i, j)=(((i−i _(center))²+(j−j _(center))² /r ^(2) * (()1+(i−i_(center))²)/r ²)^(1/2) * ((1+(j−j _(center))²)/r ²)^(1/2)

[0157] where r is the radius of curvature of the screen.

[0158] The luminance of each rectangle of a calibration grid of the kindshown in FIG. 8 is then measured by means of a screen calorimeter or bymeans of a spectro-photometer.

[0159] By comparing this luminance with the luminance at the center, itis possible to deduce a plurality of values for the function FR(i, j).

[0160] Given these values, it is then possible to calculate the missingvalues of the function FR(i, j) by interpolating using a 3rd degreepolynomial function.

[0161] FG(i, j) and FB(i, j) are obtained in the same manner.

[0162] Also, a CRT behaves like a lowpass filter, and the value of thecontrol signal applied to the electron beam reaching pixels on a givenraster line depends on the value of the control signal for the precedingpixel on the same raster line.

[0163] By way of example, FIG. 9 shows how luminance variation forsuccessive pixels situated on a given raster line itself varies as afunction of variation in control level.

[0164] More precisely, the example shown relates to the case where thecontrol level is m₁ for pixels situated at the beginning of the rasterline and changes to m₂ for the following pixels, where the value m₂ isless than the value m₁.

[0165] It is observed that the luminance W of the pixels in response tocontrol level m₂ does not drop suddenly form W(m₁) to W(m₂) but drops insubstantially exponential manner.

[0166] In other words, if the pixel control level changes suddenly fromthe value m₁ to the value m₂, then the luminance does not switchimmediately to the level W(m₂).

[0167] It is then advantageous to correct the control level inanticipation of the rise or fall time for each of the red, green, andblue channels.

[0168] The correction is performed for each raster line in the scanningdirection.

[0169] Assuming that it is desired in a given raster line to switch froma luminance W(m₁) corresponding to a control level m₁ to a luminanceW(m₂) corresponding to a control level m₂, then the level of the pixelcontrol signal is corrected by anticipation for the pixels that are tobe activated so that said pixels reach the luminance level W(m₂) morequickly.

[0170] Thus, the pixels are controlled using a control level m₃ that islower than m₂ so as to cause luminance to fall off more quickly, asshown in FIG. 10.

[0171] This predictive correction to the control level does not appearin the model shown in FIG. 5, in order to clarify the drawing.

[0172] In order to determine the time constant that makes it possible tocalculate the rise or fall time of the electron beam control signal, itis possible to proceed by displaying a first rectangle on the screen ina single color in which every other pixel of each raster lineconstituting the rectangle is controlled by means of different controllevels.

[0173] A second rectangle having the same color and the same controllevel in all of its pixels is also displayed on the screen.

[0174] Thereafter, it is possible to deduce the value of the timeconstant from the values of the pixel control levels applied to the tworectangles displayed on the screen, and thus to deduce the correctionthat should be applied to the control levels for said pixels in order toperform the above-mentioned predictive correction.

[0175] Finally, the invention makes it possible to measure the color ofobjects whether or not they are opaque, whether or not they are plane orin relief, whether or not they are moving or fixed, and it enables themeasurement to be performed without coming into contact with theobjects, with measurement being performed in transmission or inreflection, and more particularly the invention makes it possible tomeasure the color of skin and of hair.

[0176] In an advantageous embodiment, the invention further makes itpossible to reproduce without excessive distortion the color of anobject by means of a display device.

[0177] The invention also makes it possible to measure the color of eachpoint of an object, even if the object is non-uniform in color.

[0178] Naturally, the invention is not limited to the embodimentdescribed above and, in particular, it is possible to use other displaydevices, such as a printer or a liquid crystal screen.

What is claimed is:
 1. A method of correcting the response of a displaydevice having rasters of pixels, wherein, at a transition in the controllevel for pixels in the same raster line that gives rise to a variationof luminance at least between a pixel of said raster line and the pixelimmediately following it, in the raster scanning direction, the controllevel of said immediately following pixel is selected as a function ofthe rate at which the luminance of pixels situated on the same rasterline varies when the control level of said pixels varies.
 2. A methodaccording to claim 1, wherein a correction function is determined forcorrecting the non-linearities of said display device by: displaying twozones having the same color but luminances that may be different, thecolor of one of said zones being obtained by juxtaposing pixels havingdifferent control levels, while the color of the other zone is obtainedby a set of pixels all having the same control level; making theluminances of the two zones equal for an observer by acting on the pixelcontrol levels of one of the zones; and from the values of the pixelcontrol levels of each of said zones, deducing information forcalculating said correction function for correcting the non-linearitiesof the display device.
 3. A method according to claim 2, wherein saidzone made up of pixels having different control levels is rasterized. 4.A method according to claim 3, wherein said rasterized zone includesraster lines in which every other raster line is black.
 5. A methodaccording to claim 3, wherein said zone made up of pixels havingdifferent control levels includes alternating pixels in each raster linehaving a control level that is different from the control level of thepreceding pixel in said raster line.